Zuerst ersch. in: The Journal of Chemical Physics ; 139 (2013). - 234115
THE JOURNAL OF CHEMICAL PHYSICS 139, 234115 (2013)
A transferable coarse-grained model for diphenylalanine: How to represent
an environment driven conformational transition
Cahit Dalgicdir,1 Ozge Sensoy,1,a) Christine Peter,2,3 and Mehmet Sayar1,b)
1
College of Engineering, Koç University, 34450 Istanbul, Turkey
Max Planck Institute for Polymer Research, 55128 Mainz, Germany
3
Department of Chemistry, University of Konstanz, 78547 Konstanz, Germany
2
(Received 15 August 2013; accepted 27 November 2013; published online 20 December 2013)
One of the major challenges in the development of coarse grained (CG) simulation models that aim
at biomolecular structure formation processes is the correct representation of an environment-driven
conformational change, for example, a folding/unfolding event upon interaction with an interface or
upon aggregation. In the present study, we investigate this transferability challenge for a CG model
using the example of diphenylalanine. This dipeptide displays a transition from a trans-like to a
cis-like conformation upon aggregation as well as upon transfer from bulk water to the cyclohexane/water interface. Here, we show that one can construct a single CG model that can reproduce both
the bulk and interface conformational behavior and the segregation between hydrophobic/hydrophilic
medium. While the general strategy to obtain nonbonded interactions in the present CG model is to
reproduce solvation free energies of small molecules representing the CG beads in the respective solvents, the success of the model strongly depends on nontrivial decisions one has to make to capture
the delicate balance between the bonded and nonbonded interactions. In particular, we found that
the peptide’s conformational behavior is qualitatively affected by the cyclohexane/water interaction
potential, an interaction that does not directly involve the peptide at all but merely influences the
properties of the hydrophobic/hydrophilic interface. Furthermore, we show that a small modification
to improve the structural/conformational properties of the CG model could dramatically alter the
thermodynamic properties. © 2013 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4848675]
I. INTRODUCTION
Peptides and proteins exhibit a strong tendency to form
ordered aggregates. The amphiphilic nature of peptides plays
an important role, by enabling aggregation in aqueous environment or at interfaces and surfaces or by allowing them
to penetrate through or aggregate in membranes.1–3 Often
the aggregation process can be controlled via stimuli that
induce folding or conformational changes of the individual
molecules which expose polar and apolar faces of the folded
molecule.4 Or, vice versa, the aggregation of peptides or the
interaction of a peptide with a hydrophobic/hydrophilic interface (or surface) triggers a conformational change in the
molecule. Well known examples of the interplay of conformational change and aggregation or partitioning at interfaces
are the “misfolding” of proteins upon amyloid aggregation,5, 6
or more generally the induction of higher β sheet content
by aggregation7 or by the presence of an interface.8, 9 The
above phenomena are of immense importance in a large variety of fields, such as biomedical research, food science, or
material science.4, 10–14 In all these cases, combinations of
(peptide) folding, aggregation, interaction with interfaces, and
partitioning between hydrophobic and hydrophilic media are
essential elements that mutually influence each other.
a) Current address: Weill Cornell Medical College, New York, New York
10065, USA.
b) Electronic mail: [email protected]
0021-9606/2013/139(23)/234115/10/$30.00
In order to better understand and ultimately control
structure formation in peptide aggregates and peptide-based
materials, knowledge of the relevant interactions, driving
forces, pathways, and assembly mechanisms is essential.
Here, molecular simulation can be a valuable tool to provide
microscopic structural and thermodynamic insight into such
systems, perfectly complementing experimental data and analytical models. However, since such structure formation processes occur on length and time scales that are frequently inaccessible to high-resolution all-atom models alone, coarse
grained (CG) models are frequently employed—often hand
in hand with more detailed atomistic simulations.
For the problems at hand it is essential that the interplay
of aggregation, folding, and partitioning is correctly reflected
in the CG model—in particular the correct representation of
environment-driven conformational changes. This is a problem that can be viewed in the wider and more general context
of transferability challenges: simulation models are state point
dependent, i.e., they cannot per se be transferred to thermodynamic conditions, concentrations, chemical compositions,
etc., that deviate from the original conditions where they had
been parameterized. CG models are typically more state point
dependent than higher resolution models, due to the reduction
in the number of degrees of freedom where effective interactions are parameterized to capture the correct system behavior. Since understanding and solving transferability related
limitations of CG models is crucial to their applicability to
more complex (biomedical or materials science) systems, this
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FIG. 1. Diphenylalanine peptide in cis-like conformation at the cyclohexane/water interface (top) and in trans-like conformation in bulk water (bottom). Mapping of the peptide to a 4 bead CG model (PBBP, P for sidechain
and B for backbone beads) is also shown. Solvent molecules (shown as continuum for visual clarity) are mapped onto single beads: W and C for water
and cyclohexane, respectively.
topic has emerged as a high priority area in the development
of coarse graining methods.
In this study, we develop a transferable CG model for a
peptide which is capable of reproducing the correct conformational behavior in two different environments. The zwitterionic diphenylalanine peptide (FF) displays a conformational
transition from a trans-like to a cis-like state upon formation of a crystal structure composed of a hydrophobic matrix
(formed by the sidechains) with hydrophilic water channels
(surrounded by the FF backbone and charged end-groups).15
This rather unusual backbone conformation is stabilized by
the hydrophobic medium resulting from the neighboring FF
molecules’ sidechains. Here, we show via atomistic simulations that the FF molecule shows a similar conformational
transition when it is brought in contact with a hydrophobic/hydrophilic interface (see Figure 1). We aim to build a
CG model for FF, which can successfully reproduce the conformational behavior of the molecule in both bulk water and
cyclohexane/water interface. This behavior as well as its small
size and remarkable self-assembly capacity16 make FF an
ideal model system for a systematic study of rather fundamental questions regarding the interplay of nonbonded interactions and conformational behavior, specifically in the context of structure- vs. thermodynamics-based coarse graining
methodologies.
II. METHODS
Atomistic MD simulations were performed for a single
FF molecule in bulk water and in a cyclohexane/water
biphasic system representing the behavior at a hydrophobic/hydrophilic interface by using GROMACS 4.5 simulation
package.17 The conformational distributions of the atomistic
simulations of FF in both environments are used as the
references for devising the CG model. For the bulk water
J. Chem. Phys. 139, 234115 (2013)
simulation a cubic box with a dimension of 5 nm is used and
it contains 4123 water molecules. The cyclohexane/water
biphasic system for the interface simulations is performed in
a box of size 4 × 4 × 6.5 nm and contains 1601 water and
267 cyclohexane molecules. Box sizes are chosen to be larger
than twice the largest cut-off value to prevent interactions
with periodic images.
Atomistic simulations were obtained by using the
leapfrog integrator with a time-step of 2 fs. GROMOS
53a6 force-field18 is used for the FF molecule and SPC/E
model19 for water. Hydrogen bonds were constrained with
Lincs algorithm.20 Temperature is set to 298 K via velocityrescaling algorithm21 with a coupling time constant of 1 ps.
For bulk water simulations isotropic Berendsen pressure coupling at a reference pressure of 1 atm with a coupling time
constant of 1 ps and a compressibility of 4.5 × 10−5 bar−1 is
used. For the cyclohexane/water interface simulations semiisotropic pressure coupling is used such that the pressure
along the z direction is maintained at 1 atm and dimensions of
the box in x and y directions are held constant. Electrostatic
interactions are handled by particle mesh Ewald (PME)22 with
a Coulomb cutoff of 1 nm.
For the coarse-grained simulations the atomistic reference systems were mapped onto the CG model representations of the molecules by using VOTCA package,23 while
maintaining the same number of molecules. CG simulations
were performed in canonical ensemble (NVT) to avoid large
volume fluctuations. The volume of the CG box was reduced
to match the reference pressure of 1 atm: for bulk water simulations a cubic box of length 4.74 nm and for the interface
simulations a rectangular box of size 4 × 4 × 6 nm. Van der
Waals (VDW) interactions were cut off at 1.4 nm. For the CG
simulations a larger timestep (5 fs) was used, which accelerates the CG simulations by a factor of 2.5, while maintaining
correct sampling for the stiffest bond in our CG model. All
remaining simulation parameters were kept identical to the
atomistic case.
Surface tensions of the atomistic and CG interface
systems were calculated from the difference between the normal and the lateral pressure as described in detail in the
Gromacs manual,24 Eqs. (3.61) and (3.62). All molecular
visualizations were performed by Visual Molecular Dynamics (VMD) package.25
Block analysis method was used to check the convergence of the probability distributions for all systems.
Analysis results for atomistic and CG interface systems are
given in Figs. S1 and S2 of the supplementary material.26
Free energy calculations were performed by thermodynamic integration using Bennett acceptance ratio (BAR)
method.27, 28 The free energy calculation simulations are
performed under isothermal-isobaric ensembles (NPT) with
stochastic dynamic integrator,29 using Berendsen pressure
coupling.30
Umbrella sampling31 was used for potentials of mean
force (PMF) calculations where a harmonic constraint potential was applied between the centers of mass of the water
slab and the FF dipeptide. Cosine weighting32 was applied
for the center of mass of the water slab. FF dipeptide is pulled
along the direction perpendicular to the interface (z-direction)
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with a pull rate of 0.01 nm/ps with a harmonic constant of
1000 kJ mol−1 nm−2 and snapshots of the system are taken
at regular intervals. Energy minimization using the steepestdescent algorithm and an NVT equilibration for 50 000 steps
were subsequently applied to each of these snapshots which
were then used as the initial configurations for the umbrella
sampling windows. Each constraint distance for the fullatomistic and CG simulations was sampled for 10 ns and
50 ns, respectively. Weighted histogram analysis method33
was used to obtain the PMF curves.
III. TRANSFERABILITY OF CG MODELS: DIFFERENT
CHEMICAL ENVIRONMENTS
A common approach in development of coarse-grained
models is to adopt a Hamiltonian with separate terms for
bonded and nonbonded interactions:
cg
cg
U cg = Ubonded + Unonboned ,
(1)
where Ucg is the total coarse-grained potential. Similarly,
bond-length, angle-bending, and dihedral interactions are
included into the Hamiltonian as separate terms,
cg
cg
cg
Ubonded = Urcg + Uθ + Uφ .
(2)
Often then the parametrization of the different terms is done
independently, implying that the relevant degrees of freedom
are decoupled, or even if the resulting bonded and nonbonded
distributions are weakly correlated, the coarse-grained model
will successfully mimic the all atom case and display an identical or similar coupling. Hence, the strategy to devise nonbonded interactions plays no role for parametrization of the
bonded potentials. A discussion on these assumptions, where
they fail, and how the problems can be overcome has already
been provided elsewhere.34, 35
Conformational probability distributions, obtained by
mapping the atomistic configurations to the respective coarse
grained coordinates, can be used to obtain PMF for each
interaction,36–38
U cg (r, T ) = −kB T ln(P cg (r, T )/r 2 ) + Cr ,
(3)
U cg (θ, T ) = −kB T ln(P cg (θ, T )/sin(θ )) + Cθ ,
(4)
U cg (φ, T ) = −kB T ln(P cg (φ, T )) + Cφ ,
cg
cg
(5)
where P (r, T) is the bonded, P (θ , T) is the angle-bending,
and Pcg (φ, T) is the dihedral distribution. kB is the Boltzmann
constant, T is the temperature, and C’s are constant values.
Available methods for parametrization of nonbonded
interaction potentials can be divided into two general categories: (i) methods where the CG parameters are refined so
that the system displays a certain thermodynamic behavior
(typically termed thermodynamics-based)39–43 or (ii) methods
where the CG system aims at reproducing the configurational
phase space sampled by an atomistic reference system (often
misleadingly termed structure-based).36, 44–55 Inherent to the
process of coarse graining, the resulting CG models typically
suffer from representability problems:56 i.e., a structure-based
approach does not necessarily yield correct thermodynamic
properties such as solvation free energies or partitioning data
while thermodynamics-based potentials may not reproduce
microscopic structural data such as the local packing or the
structure of solvation shells. Thus, a careful assessment of
the system and problem of interest needs to be made before
choosing an appropriate coarse graining strategy.
Closely related problems arise from the limited transferability of CG models: all CG models (in fact, also all classical
atomistic forcefields) are state-point dependent and cannot
necessarily be—without reparametrization—transferred to
different thermodynamic conditions (temperature, density,
concentration, system composition, phase, etc.) or a different
chemical or molecular environment (e.g., a certain chemical
unit being part of different macromolecular chains). Structural and thermodynamic representability and state-point
transferability questions are often intimately linked, since the
response to a change in state point corresponds to representing certain thermodynamic properties, and intensive research
is currently devoted to this problem.51, 52, 57–63
To study biomolecular processes such as peptide aggregation and biomaterials structure formation, CG models are
often developed based on smaller less complex reference systems (individual peptides, subsystems, etc.). Consequently,
it is essential to achieve transferability among different concentrations and environments, to maintain correct partitioning
and solvation properties, and to reproduce coupling between
conformational behavior and environment.
In the present study, we have entirely focused on the
interplay of bonded and nonbonded interaction functions, in
particular upon the transition from a bulk water environment
to a hydrophilic/hydrophobic (cyclohexane/water) interface.
We will use the FF molecule as a model system, and demonstrate how one can parametrize a CG model which is capable
of representing the conformational properties of the molecule
in two different environments.
In its crystal structure, FF adopts a cis-like conformation,
where the two phenyl rings point in the same direction.15 In
the following, we will show that a single FF molecule in water
displays a trans-like conformation, and that the corresponding structural change can be triggered by exposure to a hydrophobic interface or aggregation. As such, the FF molecule
is an ideal model system for our study, and in order to understand and characterize the conformational preference of the
FF molecule we will first present the results of three different
atomistic simulations.
When a single FF molecule is simulated in bulk water,
the molecule adopts a trans-like conformation as shown in
Fig. 1 (bottom). Such a conformation relaxes the backbone dihedral angles, but the hydrophobic phenylalanine side chains
are separated from each other and fully hydrated. The different conformations of FF can best be characterized via a
dihedral angle between four superatoms (also indicated in
Fig. 1). Note that, later these superatoms are also going to
be used as the interaction sites in the CG model, i.e., they
reflect the mapping scheme that relates the CG beads with
the atomistic coordinates of FF. Two superatoms which are
positioned in the respective centers of mass of the phenylalanine rings will be referred to as P. The backbone and charged
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0.012
bulk water
interface
FF solution
crystal
P (φ)
0.009
0.006
0.003
-120
-60
0
φP BBP
60
120
180
FIG. 2. Probability distribution for the PBBP dihedral angle from atomistic
simulations. In bulk water (solid black line), the molecule adopts an extended
structure. At the cyclohexane/water interface the molecule adopts a cis-like
conformation (dashed blue line), highly distinct from bulk water behavior, but
similar to the crystal structure (solid red impulse). In a finite-concentration
solution of FF peptide molecules can switch from a trans-like to a cis-like
conformation (probability distribution for such a molecule is shown with
dashed brown line), when presented with a hydrophobic interface formed by
a small cluster of FF molecules.
end-groups of the FF molecule will be represented by two
identical superatoms, which are located at the positions of the
two Cα atoms and which will be referred to as B. The probability distribution for the dihedral angle among PBBP superatoms in bulk water is peaked at an extended conformation
with a maximum around −150◦ (Fig. 2, solid black line).
In atomistic simulations of a biphasic cyclohexane/water
environment, the FF molecule (initially, placed in the water
layer) quickly adsorbs to the interface, and adopts a cis-like
conformation as indicated in the representative snapshot in
Fig. 1 (top). The dihedral probability distribution at the interface (Fig. 2, dashed blue line) is very distinct from the bulk
water distribution and its maximum matches perfectly with
the dihedral adopted in the crystal structure15 (shown with the
red impulse line in Fig. 2). Phenyl side chains are driven into
the cyclohexane phase via hydrophobic forces and this force
triggers an environment mediated conformational transition
in the molecule.
The conformational transition that is observed at the
interface can also take place in bulk water with a finite concentration of FF molecules as observed in our simulations and
previously by Jeonet al.64 As the FF molecules start forming an aggregate, the hydrophobic environment, provided by
the surrounding phenylalanine side chains, lowers the energy barrier for the transition to a cis-like conformation. As
a result, a certain fraction of the FF molecules sample the
cis-like conformation during the simulation. A representative
snapshot for the conformation of such a molecule is shown
in Fig. 3. The yellow colored molecule displays a cis-like
conformation when its sidechains are in contact with a hydrophobic/hydrophilic interface of a nano-cluster of neighboring molecules. The dihedral distribution of the corresponding molecule clearly shows (Fig. 2, dashed brown line) two
peaks, one corresponding to the trans-like (characteristic for
bulk water environment) and one to the cis-like (characteristic for the interface behavior) conformation. This behavior is
not specific to a single molecule, but can be seen for many
such molecules (see Fig. S3 of the supplementary material26 ).
Note that this conformational transition is only temporary as
FIG. 3. A diphenylalanine in cis-like conformation (shown in yellow) at
the interface of a nano-cluster of diphenylalanine molecules in water. Water molecules are not shown for clarity. The nano-cluster of FF molecules
presents a hydrophilic/hydrophobic interface, which enables the transition
of the corresponding molecule to a cis-like conformation. Peptide residues
within 4 Å of the corresponding peptide are shown in red color.
seen in the time line evolution of the dihedral angle (Fig. 4).
During the 200 ns simulation, FF molecules form small
clusters, however, no stable nucleus for crystallization is
observed.
Despite the dramatic change in the dihedral angle,
the bond length and angle distributions show only modest
changes upon transfer of the molecule from bulk water to the
interface. For each bond and angle distribution the bulk and
interface results are shown in Figures 5 and 6, with solid and
dashed lines, respectively. Except for a small shift in the BB
bond length, in general bond lengths remain identical in bulk
water and interface simulations. For the bond angle distributions, a bimodal distribution is observed for both BBP and
PBB angles. Even though one can see a slight shift in peak
location and change in height, compared to the dihedral angle
these can be considered as secondary minor changes.
This small molecule represents an interesting challenge
for coarse-graining methodology. In order to design a coarsegrained model which can capture the behavior of the molecule
both in bulk water and at the cyclohexane/water interface, one
has to reconsider the assumption of the decoupling of bonded
φ
0
-180
200
150
100
50
0
-50
-100
-150
-200
100
120
140
160
t (ns)
180
200
FIG. 4. Dihedral angle among PBBP superatoms of the molecule in Fig. 3
as a function of simulation time. Unlike the peptide in bulk water (where
only trans-like conformation is observed), in a solution of peptides in water,
formation of nano-clusters with hydrophilic/hydrophobic interfaces enables
sampling of the cis-like conformation.
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J. Chem. Phys. 139, 234115 (2013)
80
60
P (r)
TABLE I. Solvation free energies of water and cyclohexane molecules for
the constituent subphases of the interface system measured from atomistic
(AA) simulations. van der Waals and electrostatic contributions, as well as
the total free energy change are listed. Lennard-Jones interactions, where parameters and σ are tuned to reproduce the measured atomistic free energy,
are used for the nonbonded interactions of water (W) and cyclohexane (C)
CG beads. Parametrization of the W-C interaction is done in two different
ways: (1) CG-FE: solvation free energy of water in cyclohexane (W/C) is
used as reference. (2) CG-ST: interaction is tuned to reproduce the surface
tension of the biphasic system.
bulk (BB)
int (BB)
bulk (PB)
int (PB)
bulk (BP)
int (BP)
40
20
0
0.34
0.36
0.38
r (nm)
0.4
0.42
FIG. 5. Probability distributions for bonds between FF superatoms (BB,
PB, and BP) from atomistic simulations in bulk water and at the cyclohexane/water interface.
Ref./Sol.
System
VdW
(kJ/mol)
Elec.
(kJ/mol)
Total
(kJ/mol)
(kJ/mol)
σ
(nm)
W/W
AA
CG
AA
CG
AA
CG-FE
CG-ST
AA
CG-FE
CG-ST
9.02
− 28.36
− 17.60
− 16.95
2.86
2.71
− 10.62
9.17
114.4
41.30
−39.24
-
− 30.22
− 28.36
− 17.60
− 16.95
2.86
2.71
− 10.62
9.17
114.4
41.30
4.64
4.0
1.33
3.19
1.33
3.19
0.288
0.547
0.455
0.455
0.455
0.455
C/C
and nonbonded interactions—where the latter encompass
solvent-solvent as well as solute-solvent interactions. The
dihedral angle PBBP displays an environment driven transition, from a trans-like conformation in bulk water to a cis-like
conformation at the interface. It cannot be taken for granted
that the combination of a dihedral potential based on the bulk
dihedral angle distribution (which strongly favors the trans
state) with the CG nonbonded interactions of P and B beads
with the solvent molecules will result in an identical change
of conformation when the molecule is placed at the interface.
One would rather expect that the transition behavior should
be strongly dependent on the type of parametrization of the
nonbonded CG model, in particular one would suspect the
nonbonded interaction of P and B beads with the solvent
molecules to be relevant. In Sec. IV, we present our approach
to developing a transferable coarse-grained model for FF, and
demonstrate its success and drawbacks.
IV. TRANSFERABLE CG MODEL DEVELOPMENT
AND RESULTS
A. CG solvent model
As we aim to analyze the conformation of the FF
molecule both in bulk water and at the cyclohexane/water interface, we used an explicit solvent CG model. Both the water
and cyclohexane solvent molecules are mapped onto one bead
per molecule (W for water and C for cyclohexane), which is
positioned at the center of mass of the corresponding solvent
W/C
C/W
molecule. For the parametrization of the nonbonded solventsolvent interactions a Lennard-Jones 9-6 potential is used.
The radii (σ ) for the Lennard-Jones interaction are matched
to the first peak in the radial distribution functions in the
AA simulations. The depth of the Lennard-Jones interaction
() is tuned to reproduce AA solvation free energies of the
respective groups, which are measured via thermodynamic
integration.65 All free energy values (both from AA and CG
simulations) that are discussed in the following, as well as
the and σ values for all solvent parameters are listed in
Table I. The respective potentials are also graphically depicted
in Fig. 7.
The pure solvent (i.e., W-W and C-C) interactions are
parametrized to match the AA thermodynamic integration results from the self-solvation of the corresponding molecules.
For the parametrization of the (mixed) W-C interaction the
case is a little more ambiguous: in principle one has two reference values from the solvation of cyclohexane in water C/W
1
0.04
bulk
int
bulk
int
P (θ)
0.03
E (kJ/mol)
0
(θBBP )
(θBBP )
(θP BB )
(θP BB )
-2
W-W
C-C
C-W CG-FE
C-W CG-ST
-3
-4
0.02
-5
0.01
0
-1
60
90
120
θ
150
180
FIG. 6. Probability distributions between the BBP and PBB superatom
triplets from atomistic simulations in bulk water and at the cyclohexane/water
interface.
0
0.2
0.4
0.6 0.8
r (nm)
1
1.2
1.4
FIG. 7. CG non-bonded interaction potentials for the solvent beads
(Lennard-Jones parameters are given in Table I). W-W and C-C interactions
are shown with solid black and blue lines, respectively. Two different potentials are used for the W-C interaction, where either the solvation free energy
of water in cyclohexane (CG-FE, dashed black line) or the surface tension
of cyclohexane/water system (CG-ST, long-dashed blue line) is taken as a
reference.
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and from the solvation of water in cyclohexane W/C, and ideally the mixed interaction should reproduce both values.
As a first approach we tuned the CG W-C interaction
to reproduce the AA solvation free energy of water in cyclohexane (W/C). The CG free energy changes linearly with
the depth of the potential , and after a few iterations we
set = 1.33 kJ/mol, which yields the CG solvation free energy of W/C to 2.71 kJ/mol—fairly close to the AA result
(2.86 kJ/mol). Using this interaction function, the CG solvation free energy of cyclohexane in water (C/W) is measured as 114.4 kJ/mol, which is an overestimation compared
to the AA result (9.17 kJ/mol), i.e., cyclohexane beads are
too strongly repelled from the aqueous phase. If, alternatively,
one chooses to tune the CG interaction potential for W-C to
match the C/W AA solvation free energy, one obtains a very
deep W-C interaction (data not shown). This model results
in a negative W/C solvation free energy, i.e., the solvation of
water in cyclohexane becomes highly favorable, destabilizing
the interface. Hence, this model clearly leads to unphysical results. It turns out that with the approach chosen one cannot simultaneously reproduce both the W/C and the C/W solvation
free energy in the CG simulations. The first CG model—tuned
based on the W/C solvation free energy—will be referred to
as CG-FE solvent model in the remainder of the text.
Given the ambiguity discussed above we decided to alternatively tune the W-C interaction potential to reproduce the
surface tension of the cyclohexane/water system (with the target surface tension from AA simulations being 50.2 mN/m).
The resulting model will be referred to as CG-ST solvent
model (see Fig. 7, the potential is significantly deeper than
CG-FE but not as deep as the discarded free-energy model
tuned from the C/W solvation). Compared to the CG-FE solvent model, which yields a surface tension of 157 mN/m,
CG-ST by construction better represents the interface properties. However, this is achieved at the cost of the solvation
free energies in the corresponding subphases of the system:
the solvation free energy for W/C and C/W are calculated as
−10.62 kJ/mol and 41.30 kJ/mol, respectively (see Table I).
As a further comparison of the CG solvent models with AA
data, radial distribution functions and density profiles for water and cyclohexane beads are shown in Figs. S4 and S5 of the
supplementary material.26
For the parametrization of FF in the interface system, in
Sec. IV B we will proceed with both CG solvent models, CGFE and CG-ST. Note though that the only difference between
the models is the interaction between the CG cyclohexane and
water beads, i.e., the interaction that governs the behavior of
the interface.
J. Chem. Phys. 139, 234115 (2013)
Since the solvent superatoms are not polarizable and in the
present simulations no peptide-peptide interactions are considered, the B beads on the peptides do not carry any charge.
With this mapping the CG FF model requires 3 bond, 2
angle, and 1 dihedral angle as bonded interactions, and nonbonded interaction potentials between the peptide and the solvent molecules. As a further simplification, we ignored the
small differences in bond and angle distributions between
bulk water and at the interface, and focus primarily on the
dihedral angle. The interaction potentials for bonds (PB, BP,
BB) and angles (PBB, BPP) are obtained via Boltzmann inversion (Eqs. (3)–(5)) of the corresponding probability distributions in bulk water (see Figs. 5 and 6). The bonds are
represented via harmonic potentials (see Table S1 of the supplementary material26 ), whereas the angle and dihedral potentials are represented in tabular form (see Figs. S6 and S7
of the supplementary material26 ). The resulting distributions
from the CG model and comparison with the atomistic bulk
and interface simulations are given in Figs. S8 and S9 of the
supplementary material.26 For the bond and angle distributions the CG model reproduces the AA system well. Hence,
we only focused on the dihedral angle PBBP.
Since the PBBP dihedral angle is coupled to the
nonbonded interactions, we first describe the initial
parametrization of the nonbonded interactions between
the peptide and the solvent molecules. Similar to the solvent
parametrization, these are also derived based on the solvation
free energy of fragments representing the respective groups
obtained via thermodynamic integration. Note that the derivation of parameters based on molecule fragments is potentially
problematic since free energy is not per se additive, but these
fragment-based parameters serve as a good initial guess.
The free energy change upon transfer of the relevant group
from vacuum into the bulk solvent medium is obtained from
AA simulations. The relevant solvation free energy values
measured from AA simulations, and the Lennard-Jones
parameters for the matched CG interaction and the resulting
CG free energy values are shown in Table II. Ethyl-benzene
TABLE II. Solvation free energy of FF fragments (that are mapped to the
CG beads) in the respective solvents obtained from AA simulations. CG
beads’ nonbonded interactions are represented via Lennard Jones interactions, where the depth and radius σ of the interaction are fitted to reproduce
the AA free energy. Results with the modified P/C interaction are also shown
for the different solvent models used: CG-FE and CG-ST.
Ref./Sol.
P/W
P/C
B. CG FF model
The CG model for FF used here is composed of four
beads as already described and depicted in Fig. 1, with masses
of the sidechains assigned to the P beads and the mass of
the backbone atoms and the end groups distributed equally to
the two B beads. As discussed above, the environment-driven
conformational transition of FF can be successfully represented in this mapping scheme via the PBBP dihedral angle.
mod-P-C CG-FE
mod-P-C CG-ST
B/Wa
B/C
VdW
System (kJ/mol)
AA
CG
AA
CG
CG
CG
AA
CG
AA
CG
Elec.
(kJ/mol)
Total
σ
(kJ/mol) (kJ/mol) (nm)
− 9.19
− 0.11
− 0.21 2.81
− 23.36
− 23.21 4.515
− 54.30 7.00
− 72.59 8.40
28.81 − 283.6 − 254.8
− 119.0
− 119.0 10.31
− 18.62
− 18.62
− 9.78
− 9.78 4.0
9.08
− 0.21
− 23.36
− 23.21
0.288
0.547
0.547
0.547
0.288
0.547
a
For the B/W interaction CG bead is tuned to reproduce half of the hydration free energy
of zwitterionic diglycine.
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Dalgicdir et al.
J. Chem. Phys. 139, 234115 (2013)
0
0.02
-2
0.016
W-W
C-C
B-W
P-C
mod-P-C
-6
-8
-10
-12
P (φ)
-4
0
0.2
0.4
0.6 0.8
r (nm)
1
AA
CG-nodih
CG-nodih-reduced P
CG-int-dih
CG-bulk-dih
0.012
0.008
0.004
1.2
0
-180
1.4
FIG. 8. CG nonbonded interaction potentials between the FF and solvent
beads (Lennard-Jones parameters are given in Table II). For the P-C potential
the modified CG interaction is also shown for CG-ST solvent model (dashed
brown line), which corrects the dihedral distribution at the interface (see text
for details).
is used in atomistic free energy calculations to parametrize
the CG P beads. For the B beads, the solvation free energy of zwitterionic diglycine is computed since a smaller
charge-neutral atomistic reference would have been difficult
to construct. Half of its transfer free energy is used for the
initial parameterization of the CG model. Peptide-peptide
B-B and B-P interactions are not included, since we are only
interested in a single FF molecule. The P-P interaction is set
as a purely repulsive Lennard-Jones potential (short ranged
interaction with a cut-off at the minimum), representing
only the excluded volume effect in the CG simulations. The
nonbonded interaction potentials which play an important
role in the FF molecule’s conformational behavior are shown
in Fig. 8.
C. Parametrization of the dihedral potential
In this section, the parametrization of the CG dihedral
potential PBBP and the performance of the FF CG model in
the CG-FE and CG-ST solvent models will be discussed. We
start by analyzing the behavior of the CG model in bulk water
in the absence of an explicit dihedral potential. In bulk water,
both CG solvent models are identical since the W-C interactions are not relevant.
The first problem arises from the spherical bead representation of the phenylalanine side chain, which has a planar
geometry. The single-bead representation of P prevents
penetration of CG water beads into the space between the
two sidechains, and as a result, unlike the AA bulk water
simulation, the CG simulation yields a cis-like conformation
(Fig. 9, dashed brown line). This can be overcome if the
diameter of the P-W interaction is reduced from (initial)
0.5 nm to 0.28 nm which corresponds to the σ of the W-W
interaction. With these “reduced size” P beads, the CG model
yields a uniform dihedral angle probability distribution
(Fig. 9, solid brown line). In other words, with all other
bonded and nonbonded interactions defined, this CG FF
model has no dihedral preference on its own in bulk water.
Therefore, to capture the atomistic behavior in bulk water, one
can simply Boltzmann invert the atomistic dihedral probability distribution in bulk water to obtain an effective dihedral
potential. After adding this dihedral potential, the CG model
-120
-60
0
φP BBP
60
120
180
FIG. 9. Bulk water: Comparison of PBBP dihedral angle probability distribution from CG simulations with the atomistic reference (solid-black line).
Without an explicit dihedral potential, single-bead representation (see text) of
the P beads leads to a cis-like conformation (dashed brown line). When the
size of the P beads is reduced, a flat dihedral distribution is obtained (solid
brown line). Thus, dihedral potential obtained via Boltzmann Inversion (BI)
of the atomistic reference in bulk water (dashed blue line) reproduces the correct behavior. On the other hand, BI of the interface distribution fails in bulk
water (solid-blue line).
is perfectly capable of representing the bulk water behavior,
as shown in Fig. 9 (dashed blue line). Alternatively, if one
obtains a dihedral potential by Boltzmann inverting the AA
simulation’s dihedral distribution at the interface, a cis-like
conformation is observed also in bulk water as expected (solid
blue line in Fig. 9), i.e., not the appropriate bulk behavior.
Next, we use this CG model which reproduces the bulk
water behavior (with reduced size P-W interaction and dihedral potential obtained from BI of the bulk water distribution)
for the biphasic system with a cyclohexane/water interface.
Figure 10 shows that in the CG-ST solvent model the dihedral
distribution at the interface is not correct: the FF molecule
remains in a trans state (Fig. 10, solid brown line). In the
CG-FE solvent model (Fig. 10, solid blue line), however, the
FF molecule undergoes a transition towards a cis-like state,
with a dihedral distribution that is shifted compared to the AA
result, but that nevertheless at least qualitatively displays the
0.012
AA
CG-FE
CG-ST
CG-FE mod-P-C
CG-ST mod-P-C
0.009
P (φ)
E (kJ/mol)
234115-7
0.006
0.003
0
-180
-120
-60
0
φP BBP
60
120
180
FIG. 10. Cyclohexane/water interface: Comparison of PBBP dihedral angle probability distribution from CG simulations with the atomistic reference
(solid black line). CG model uses reduced P-W interaction radius and dihedral potential based on BI of atomistic bulk water dihedral distribution.
The CG solvent model with surface tension tuned W-C interaction fails to
capture the correct dihedral behavior (CG-ST, solid brown line), whereas the
W-C interaction tuned to reproduce solvation free energy of a water molecule
in cyclohexane solvent (CG-FE, solid blue line) yields a fairly close result.
By increasing the attraction for the P-C interaction both CG models can be
enhanced to yield a better match with the AA result (dashed blue and dashed
brown lines for CG-FE and CG-ST solvent models, respectively).
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Dalgicdir et al.
J. Chem. Phys. 139, 234115 (2013)
6
AA
CG-FE
CG-ST
CG-FE mod-P-C
CG-ST mod-P-C
5
P(r)
4
20
V (r) (kJ/mol)
234115-8
3
2
-20
AA
CG-FE
CG-ST
CG-FE mod-P-C
CG-ST mod-P-C
-40
-60
1
-80
0
-1
-0.5
0
r (nm)
0.5
1
FIG. 11. Probability distribution for the distance of FF from the interface.
Unlike the AA simulation (solid black line), where the molecule is placed
right at the interface, CG model yields a submerged FF molecule with both of
the tested solvent models (CG-FE and CG-ST shown with solid blue and solid
brown lines, respectively), with CG-ST model displaying looser adsorption to
the interface. Modified P-C interaction enhances both cases (dashed lines),
where modified CG-ST case yields almost a perfect match with atomistic
results.
correct conformational transition. This is in a sense quite a
remarkable difference since the two solvent models only differ in the interaction between cyclohexane and water, i.e., the
interface properties, there is no difference in the direct interaction between the peptide and the solvents. Nevertheless, one
of the two models is showing—qualitatively correctly—the
environment-driven conformational transition, and one is not.
Remarkably, the model that does show the transition is not
the model that had been parametrized according to the surface
tension, i.e., the interface behavior. In order to understand this
better, we have proceeded to analyze the behavior of FF at the
interface further, and to investigate what would have to be
done to reproduce the conformational change at the interface
in both solvents.
As far as the positioning of the FF molecule at the interface is concerned, in both CG solvent models the FF molecule
is submerged somewhat towards the water side of the interface
compared to the AA reference, with the CG-FE model being
closer to the AA result (see Fig. 11, solid blue and brown
lines). For the orientation of the molecule with respect to the
interface, the CG model does not display the broken symmetry observed in the atomistic simulation. The distribution of
the orientation angle γ has a maximum at γ = 90◦ in the CG
model (see Fig. 12). Here, γ denotes the angle between the
0.024
AA
CG-FE
CG-ST
CG-FE mod-P-C
CG-ST mod-P-C
0.018
P (γ)
0
0.012
0.006
0
0
30
60
90
120 150 180
γ
FIG. 12. Probability distribution for the orientation angle (γ ) of the molecule
with respect to the interface for atomistic (solid black line) and CG model
with two different solvent models (solid blue line for CG-FE and solid brown
line for CG-ST). Upon modification of the P-C interaction, both CG-FE and
CG-ST cases yield a narrower distribution compared to the atomistic results
(dashed lines).
-2
-1.5
-1
-0.5
r (nm)
0
0.5
FIG. 13. Potential of mean force, V (r), for the transfer of FF from bulk water
to the cyclohexane/water interface. CG-FE solvent model yields the closest
match to the atomistic result in terms of depth (solid blue line), whereas CGST solvent model displays a weaker attraction towards the interface. In both
cases the minimum is shifted towards the water side of the interface. Modification of the P-C interaction pulls down the PMF curve to much deeper
values, largely overestimating the adsorption energy (dashed lines).
interface normal and the normal of a plane fitted to the four
beads of the CG peptide. With the lower resolution of the CG
model, failure of the model to capture this broken symmetry
is not surprising.
Since we assumed that the conformational transition of
the molecule is driven by the segregation forces that are only
present at the interface, we calculated the potential of mean
force for pulling the FF molecule from the middle of the water layer to the interface. The PMF curves corresponding to
the AA and CG system are shown in Fig. 13. Since we are
mainly interested in the transfer from the bulk water phase
to the interface, we limited our PMF calculations to a distance range up to 0.8 nm across the interface. The atomistic
system shows a 20.6 kJ/mol change in free energy upon adsorption of the molecule to the interface. The minimum of
the potential is positioned right at the interface, in agreement
with the free simulation results shown in Fig. 11. The CGFE model (Fig. 13, solid blue line) yields a similar adsorption free energy (23.6 kJ/mol). However, unlike the atomistic system, the potential minimum is located slightly below
the interface (also in agreement with the results shown in
Fig. 11). The CG-ST solvent model shows a weaker adsorption to the interface (solid brown line), i.e., in this aspect
it shows less agreement with the atomistic reference (solid
brown line).
An interesting difference between the CG-FE and CG-ST
results is that the CG-FE PMF curve rises more steeply compared to the AA PMF when the molecule is dragged into the
cyclohexane phase. The analysis of the trajectory shows that
this is a direct consequence of the hydration shell of the FF
molecule. For the CG-FE solvent model, the reduced W-C
interaction potential results in a stripping off of all the water molecules in the hydration shell of FF as the molecule
is pulled out of the water layer. In contrast, the CG-ST successfully mimics the AA results in this regard and maintains
part of the hydration shell of the FF molecule as the molecule
enters the cyclohexane phase.
The results shown so far suggest that tuning the dihedral
potential alone is not necessarily sufficient to capture the desired conformational behavior for the CG system in both bulk
water and at the cyclohexane/water interface. Even though
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234115-9
Dalgicdir et al.
the affinity towards the interface (i.e., the PMF of the entire molecule) is reproduced fairly nicely with the fragmentbased free-energy-tuned peptide-solvent interactions, the
cis-trans conformational transition is not necessarily correctly
represented by the CG model. Disconcertingly, in the present
system the outcome appears to be depending on the solventsolvent interactions, i.e., on parameters that do not involve
the peptide at all and that may in some more complex scenarios of many-component systems not be free for parameter
changes.
Therefore, we have investigated what would have to be
done (involving the peptide-solvent interactions) to reproduce
the correct conformational behavior in both solvent scenarios. We found that one possible solution involves increasing
the strength of the interaction between the cyclohexane and
phenylalanine side chain beads (see Fig. 8, dashed brown line,
labeled mod-P-C), so that the segregation forces are further
enhanced. Since the P-C interaction is used only in the interface simulation, the bulk water behavior of the molecule
remains unaffected. For each of the two CG solvent models
the depth of the modified P-C (listed in Table II) is chosen
such that at the interface the AA cis-dihedral distribution is
more or less exactly reproduced—overruling the dihedral potential which favors a trans-like conformation. Interestingly,
for both CG solvent models the interaction has to be substantially deepened to achieve the effect, even though in the
CG-FE case the unmodified model had already shown a qualitatively quite acceptable distribution. As shown in Fig. 10
with dashed lines, after this modification the CG model correctly captures the interface dihedral distribution with both
CG solvent models. The position with respect to the interface
is also improved compared to the original CG model (Fig. 11,
dashed brown line), surprisingly CG-ST model now outperforming the CG-FE model. The orientation of the molecule
still yields a maximum at γ = 90◦ (Fig. 12) and is much
narrower compared to the AA result. However, this improvement takes place at the cost of the adsorption free energy:
the modified CG model (by construction—due to the stronger
P-C affinity) exhibits a much larger driving force towards the
interface (Fig. 13).
V. CONCLUSIONS
The results presented in this paper show that with respect
to sampling of conformations, transferability of CG models
cannot be taken for granted. The model system, diphenylalanine, displays distinctly different conformations in bulk water
compared to the cyclohexane/water interface. The pseudo dihedral angle, which we labeled as PBBP favors a trans-like
conformation in bulk water, whereas it switches to cis-like
conformation at the cyclohexane/water interface. The same
conformational transition is also seen upon aggregation of
FF molecules into nano-tubes. Hence, if one desires to capture the surface adsorption or aggregation of such a molecule
via a CG model, the model should display an identical
conformational transition.
Here, we showed that such a conformational cis/trans
transition is not automatically captured by the CG model,
even if the partitioning forces that are the origin of this
J. Chem. Phys. 139, 234115 (2013)
conformational transition form the basis of the parametrization of nonbonded interactions. Even more so, the ability to
reproduce the conformational transition may depend on parameters of the solvent models that do not involve the peptide
at all and that merely affect the behavior of the interface. Between the two different solvent models we have tested, the
CG-ST solvent model, where the mixed solvent-solvent interactions had been parametrized according to surface tension,
did not induce the conformational transition at the interface at
all, even though the model showed quite good results for the
surface affinity (see PMF curve). The CG-FE model on the
other hand, where the water cyclohexane interaction is parameterized to mimic the solvation free energy of water in cyclohexane, yields a fairly good result in capturing the dihedral
distribution at the interface and representing the adsorption
free energy from water to the cyclohexane/water interface.
Finally, we showed that the interface dihedral distribution for both of these CG solvent models can be corrected
by reparametrizing the P-C interaction. This modification not
only affects the conformational behavior, it also significantly
improves the position of the FF molecule at the interface.
However, one sacrifices the correct adsorption strength of the
FF to the interface, as seen in the PMF curves in Fig. 13.
The crucial role that the correct representation of the water
interface has on the conformational transitions of the peptide
suggests that, it will be eminently interesting to study conformational transferability in a water model such as the one
from Molinero and Moore66 in the future. Improved representation of structural and thermodynamic properties of water
could potentially eliminate the need for reparametrization of
peptide-solvent interactions.
The entire study shows that one has to reconsider the
separation of bonded and nonbonded interactions for the
parametrization of CG models. The subtle interplay between
the conformational preference of the molecule (that should be
mainly “covered” by the dihedral angle potential), the solvation properties of its fragments (that should be mainly “covered” by the various nonbonded interaction potentials), and
even interactions in the environment that do not directly affect
the solute molecule at all have to be taken into account. In the
present paper, we have shown that one way to correctly capture the conformational preference is to adjust the nonbonded
interactions, rather than playing with the dihedral potential.
This modification corrects the conformational preference of
the molecule at the interface and reproduces the conformational transition, but one sacrifices the exact reproduction of
the adsorption free energy to the interface.
The parametrization presented here was intended mainly
to understand the interplay of the relevant driving forces for
such an environmentally-driven conformational transition and
how they can be correctly accounted for in the CG model.
We are aware that the four-bead CG model used in this paper may be problematic for reproducing the full aggregation
behavior including the formation of microscopically accurate
structures, since the backbone is likely to be too coarsely
represented and sidechains might fail to capture the aromatic nature of the phenylalanine sidechains. Representation
of sidechain conformations could potentially be improved by
using an angle dependent potential.67 Alternatively, a similar
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234115-10
Dalgicdir et al.
parametrization can be introduced for the MARTINI representation of FF molecule, which has been recently shown to
exhibit interesting aggregation behavior for FF.68 In the long
run it would also be interesting to use a solvent free model to
study large scale aggregation (without an interface). In that
case the crucial interactions that will have to be balanced
are the hydrophilic and hydrophobic interactions between the
various peptide beads.
ACKNOWLEDGMENTS
M. Sayar, C. Dalgicdir, and O. Sensoy would like to
thank TUBITAK (Grant No. 212T184). We also thank the
Max Planck Society for financial support through the Partner Group Agreement with Professor Kurt Kremer’s Theory
Group at MPIP, Mainz. C. Peter gratefully acknowledges financial support by the German Science Foundation within
the Emmy Noether Programme (Grant No. PE 1625/1). We
are grateful to Christoph Globisch and Alok Jain for many
valuable suggestions.
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